All the predictions of the 100 channels are shown in the tables of
ref.[1]}. The prediction of branching ratio of the
pure annihilation process \(D_s^+\rightarrow \pi ^+\pi ^0\)  vanishes in the pole
model within the isospin symmetry. It is also zero in the
diagrammatic approach in the flavor SU(3) symmetry. Simply, two
pions can form an isospin 0,1,2 state, but 0 is ruled out
because of charged final states, and isospin-2 is forbidden for the leading order \(\Delta C=1\)  weak decay.
The only left s-wave isospin-1 sate is forbidden by Bose-Einstein statics. In the pole model language, \(G\)  parity is violated
in the isospin-1 case. Therefore, no annihilation
amplitude contributes to this mode.
